proof of the fundamental theorem of calculus math 121 calculus ii djoyce spring 2013 1 the statements of ftc and ftc before we get to the proofs let s rst ...
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...Proof of the fundamental theorem calculus math ii djoyce spring statements ftc and before we get to proofs let s rst state fun damental inverse when do prove them ll is what oresme propounded back in sometimes called second fundamen tal but that gets history backwards if f continuous on then zabf x dx b a other words an antiderivative acommonnotation for there are stronger these theorems don t have continuity assump tions stated here ones function closed interval its accumulation dened by zaxf dt dierentiable derivative frequently conclusion this written d z xf note dierent variable used integrand since already has meaning logicians computer scientists comfortable using same two purposes they resort concept scope order pull o it usually easier make sure each only one thus use as limit integration inside integral our first all integrable say does exist weneed show denition derivatives lim h hf equals although complete would consider both cases look at case similar more complicated negat...